purity, loyalty and authority are not only culture-specific, also political tribe-specific, and there are huge mistake potentials here, what is authority for one is a proper expert for another, what is purity for one is understandable revulsion over an immoral act for the other, what one sees as disloyalty can be loyalty to a non-standard group and so on.
Note that you just made an argument for these being terrible bases for public and social policy in a diverse society.
Yes. And you can go two ways from there. Either you can try to eliminate them, but then you meet the issue that for most folks it is incredibly difficult to make a difference between policy and values as both are approached from an "I cheer for X" angle. If succesful, you end up with a society that does not have a culture. From this viewpoint I feel for the conservative case. It is very, very weird to try to build a society without culture, it is as if it was not meant for human brains. And it would be very good if people could see a clear dif...
In 2011, InquilineKea posted a Discussion topic on YourMorals.org, a psychology research website which provides scores of psychology scales/inventories/surveys/tests to the general public to gather large samples. Niftily, YourMorals lets users sign up for particular groups, and then when you take tests, you can see your own results alongside group averages of liberals/conservatives/libertarians & $GROUP. A lot of time has passed and I think most LWers don't know about it, so I'm reposting so people can use it.
The regular research has had interesting results like showing a distinct pattern of cognitive traits and values associated with libertarian politics, but there's no reason one can't use it for investigating LWers in more detail; for example, going through the results, "we can see that many of us consider purity/respect to be far less morally significant than most", and we collectively seem to have Conscientiousness issues. (I also drew on it recently for a gay marriage comment.) If there were more data, it might be interesting to look at the results and see where LWers diverge the most from libertarians (the mainstream group we seem most psychologically similar to), but unfortunately for a lot of the tests, there's too little to bother with (LW n<10). Maybe more people could take it.
You can sign up using http://www.yourmorals.org/setgraphgroup.php?grp=623d5410f705f6a1f92c83565a3cfffc
All quizzes: http://www.yourmorals.org/all_morality_values_quizzes.php
Big 5: http://www.yourmorals.org/bigfive_process.php
(You can see some of my results at http://www.gwern.net/Links#profile )